The incident happened last week in Ponte de Sor, central Portugal, following a brawl between locals and pupils at a nearby flight school where one of the twins is enrolled, according to Portuguese media yesterday.
A source close to the investigation said the 17-year-old sons of the Iraqi ambassador in Lisbon, Saad Mohamed Ridha, were arrested but then released because they had diplomatic immunity.
Portugal's Foreign Minister Augusto Santos Silva said his country may request that Iraq remove the diplomatic immunity so that the pair can be prosecuted.
The Iraqi twin brothers, Haider and Ridha Ali, were interviewed on the Portuguese television channel SIC, with the former expressing remorse while the latter claimed to have been defending himself from attack.
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"I am ready to fully accept the responsibility of my actions, I don't know what is the Iraqi government's reaction. I am not hiding under the umbrella of the diplomatic immunity," Haider Ali said, offering his "deepest apologies" and insisting he wouldn't leave Portugal.
His brother Ridha said the pair had been "attacked by five or six persons".
Ridha Ali added that "Ruben" saw them a little later and spoke in "a very aggressive tone... He hit me again in the face and on my shoulder".
"I felt insulted and couldn't take it anymore... So I ran after him, I punched him and a minute later, he was down on the ground. I kicked him a few times when he was down on the ground."
The Iraqi foreign ministry said it was following the case "with close concern" and had launched a probe to gather "details concerning this incident and gather information from mass media".
The foreign ministry added it was keen to maintain "its good reputation" and the solid relations it enjoys with Portugal.